Question

Two spherical objects differ in size and mass. Object A has a mass that is eight times the mass of B. The radius of object A is twice the radius of object B. How do their densities compare?

a) Density of A is half the density of B.
b) Density of A is the same as the density of B.
c) Density of A is four times the density of B.
d) Density of A is eight times the density of B.

Answer 1

The density of A is the same as the density of B.

Step-by-step explanation:

The density of an object is defined as the ratio of its mass to its volume. In this case, we have two spherical objects, A and B. Given that the mass of A is eight times the mass of B and the radius of A is twice the radius of B, we can compare their densities.

Let's assume the mass of B is m, so the mass of A is 8m. The volume of a sphere is proportional to the radius cubed. Since the radius of A is twice the radius of B, the volume of A is 8 times the volume of B.

Therefore, the density of A will be (8m) divided by (8 times the volume of B), which simplifies to the same value as the density of B. Hence, the density of A is the same as the density of B (option b).